A really good book introducing the subject of entanglement. The first 2 hours go through a basic history of Quantum Mechanics, but provides some interesting vignettes of Plank, Schrodinger, Heisenberg, and Von Neumann. 2 fun facts I pulled away from this part: Plank, like Einstein, didn't ever believe Quantum theory was anything more than a statistical approximation, and he came about his name-sake constant purely through empirical means. He never realized it may end up being a universal invariant. Second interesting fact on the fathers of QT, Schrodinger was a chronic philanderer, who had an illegitimate child, who himself fathered a noted particle physicist many years later.
From here, the book focuses on the real meat of the subject matter, namely Bell's Inequality, and the mathematical and experimental results predicting this finding. As a subject matter layman myself, it is deeply striking to learn the fact that both the Heisenberg Uncertainty Principle and the Bell Inequality, are simple extensions of properties of Hilbert Spaces as the author demonstrates in the text. Hilbert spaces are a type of abstract algebra in pure mathematics.
According to the author, the algebraic structures that show these results are the Non-commutativity of operator products for the Uncertainty principle, and a proof that no dispersion free states exist in Hilbert Spaces of dimensions greater than or equal to 3, for Bell's inequality. I have not done the proof by hand myself, so I'll take his word on that. Unfortunately, besides broadly stating what a dispersion-free state is, which he summarizes as a state with only non-stochastic components, not much is explained about how they are derived/defined with respect to Hilbert Spaces. This is where I suspect a proper textbook on QM would come in handy.
Despite the failure in some of the descriptive details, these two results should strike the listener to their core. The fact that the corpus of QM can be fitted into such a neat/clean mathematical structure, is a prime example of the often quoted "unreasonable effectiveness of mathematics" from Eugene Wigner. In fact, as the author states int he book, QM is accurate up to numerical precision of 40 decimal places for behaviours of objects less than 10 nanometers. It's also never been inconsistent with any experimentation up to now.
The consistency of the theory with empirical data is no small feat, as there are many subjects and theories that attempt to extend from pure abstraction but fail miserably when corresponding to real data. Mathematical economics comes principally to mind when thinking of examples. There, one has a subject that front-loads much more abstraction than QM, or even QFT, or any of the modern day iterations of those ideas, and yet can scarcely claim any predictive power whatsoever. That subject is almost a total failure as a predictive science in its purported domain. The fact that the founders of QM extended a theory from abstraction to reality, while maintaining empirical consistency, will remain a rare jewel in human knowledge for some time I suspect.
Some, however, would contend that this is an anachronistic characterization, as linear algebra and quantum theory are contemporaneous. Therefore, the abstract algebra which founds the Hilbert Space Theory came after the experimental findings of QM. So one would be hard-pressed to claim that QM sprung forth from pure abstraction.
This may be true about the Uncertainty Principle, although, it should be noted that Heisenberg independently derived matrix algebra, and the Linear Algebra was developed often unknown to early 20th century physicists. However, it doesn't seem to be true about the Bell Inequality, and the corresponding proof, establishing that entanglement was an actual physical phenomenon.
This book goes over a lot of the above discussion and much more, including the scientific and philosophical discussions of the EPR paradox, and how this motivated the study of entanglement. This was itself posed as a sort of proof by contradiction from Einstein, Rosen, and Podolsky. This book is really, a fascinating history of these ideas. In the end, Einstein could not jettison the notion of scientific realism to accept non-locality, entanglement, or QM, as a whole. A bit tragic, as it may come about that his EPR Pair paper might end up being his most impactful work in the grander context of modern science.
In summary, this book would serve an excellent supplement and guidebook for a more technical text, as it does delve fairly deeply for a lay text into the actual mechanics of QM. It puts many abstract and experimental results into historical context and time order, which I believe helps one learn the material. Highly recommend